Classical Electrodynamics · Problem 5.23

Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws — John David Jackson

Physics — E&M · magnetized-cylinder-adhesion-force

Problem

A right circular cylinder of length

L

and radius

a

has a uniform lengthwise magnetization

M

. (a) Show that, when it is placed with its flat end against an infinitely permeable plane surface, it adheres with a force

F = 2\mu_0 a L M^2\left[\frac{K(k) - E(k)}{k} - \frac{K(k_1) - E(k_1)}{k_1}\right]

where

k = \frac{2a}{\sqrt{4a^2 + L^2}}, \qquad k_1 = \frac{a}{\sqrt{a^2 + L^2}}

(b) Find the limiting form for the force if

L \gg a